I was elementary-school aged (maybe 9?), in the dentist's waiting room with Mom, waiting for my turn under the tooth scraper. I found some puzzles in a Highlights magazine and was struggling with "If a basketball weighs 4 pounds plus half its own weight, how much does it weigh?"

The answer in the back of the magazine didn't even use algebra, it just said something like "Well if the total weight is something plus half of itself, that something must be the other half. The two halves must be equal, so it's 4 + 4 = 8." And it makes perfect sense once you think of it that way.

I showed the problem to Mom, and she didn't waste any time trying to think of a tricky way of looking at the problem...instead, she just wrote:

W = 4 + (1/2) W
W - (1/2)W = 4
(1/2) W = 4
W = 8

What? She got the right answer in seconds, and apparently without any hard work or struggle for insight. That was really cool. I didn't understand exactly how she had done it, but I understood that she had a dependable and broadly-applicable tool called "algebra" that I didn't have, and I wanted it, too.

8th Grade

I had my other algebra epiphany in 8th grade. We were studying quadratic equations (parabolas), and the math book said "Here, trust us, this equation will tell you the height of a ball at time T, given its initial height and its initial upward speed." Something like:

H = H0 + VT - 16 T2

The ball was being thrown upward from on top of a cliff, and it was going to fall down farther and eventually hit the ground. So we were supposed to solve for T to find out when the ball was at ground level. I was expecting, of course, to get a single answer, but since I was solving an equation with a T2 in it, I got two answers.

One of the answers was a negative number of seconds; we were supposed to ignore it and just use the positive one. What stunned me at the time was realizing that the negative answer was meaningful, as the extrapolation of the ball's path backwards in time, to when it would have been thrown from ground level (inside solid rock, perhaps) to follow the same path. The simple equation was more powerful than the book had led me to believe.

Fun With a Saw

When I was in Junior high, we were camping way up in the mountains, and I was using a bow saw with my left hand while steadying the log with my naked right hand.

Dad says: "Dave, do you think you might want to wear a glove while you're sawing that log?"

Dave says: "No, I'll be OK."

Dave: Promptly lets the saw slip, gouging his own right index finger in a couple of places. Ouch.

Luckily, no stitches were required; it would have been quite a drive to the nearest clinic. Dave is now more careful, and tries harder to listen to Dad.